A RSL club has faced an extraordinary attack from ACT Labor MLA Bec Cody over tiles on the walls of its men's toilet which depict Indigenous men — criticism the club says is "ridiculous" and "out of order".

At the end of today's sitting in the ACT Legislative Assembly, new member for Murrumbidgee Bec Cody used her speech, under parliamentary privilege, to blast the Sussex Inlet RSL near Jervis Bay on the South Coast.

She said her husband had told her about four tiles installed either side of the urinal in the men's bathroom, depicting Aboriginal men near rocks and with boomerangs.

Ms Cody took offence to the tiles and described the leaders of the RSL as either "racist" or "standing by racists".